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If mn plus one is divisible by 24 . Prove that m plus n is also divisible by 24

If mn plus one is divisible by 24 . Prove that m plus n is also divisible by 24

Grade:9

1 Answers

mycroft holmes
272 Points
7 years ago
mn+1 is divisible by 3 and 8.
 
If mn+1 is divisible by 3, you can easily see that we need m and n to be of the form 3s+1 and 3t-1 or vice versa. So m+n is divisible by 3
 
If mn+1 is divisible by 8, then either m and n are of the form 8s+1 and 8t-1 in some order, or 8s-3,8t+3 . Again m+n is divisible by 8
 
So, m+n is divisible by 3 and 8 and hence by 24

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